I heard (I think when lurking this forum) that lots of schools are now letting you bargain over the amount of finaid/scholarship you get when going to their school. I think UCLA's dean even explicitly states that.

I'd love to go to a T14 law school, but the amount of money is pretty important to whether I can afford going there or not. Is there a strategy to being able to get a better deal from a T14 law school, like applying to competitive non-T14 law schools and then using them as a bargaining chip? Or are there certain T14 schools that will provide me more finaid because of my decent numbers?

Apply to as many schools as you can and leverage them against each other. It is a tedious process and there is no real formula to success but by and large it works. Not every school will negotiate, some schools only take offers of peer schools or higher into consideration, some consider huge offers from worse schools and then offer you something but less, while others take into account demonstration of need and desire to attend.

The most reliable trend is that schools in the T5-13 are responsive to offers from each other and 11-14 have been known to be compelled by 15-25 offers. Again it's not a hard and fast rule and it kind of depends how much you are asking for and what day you catch them on. They may have funds available and a need for your numbers one week and the next week have those funds allocated and/or need a splitter or a minority or whatever.

I've seen success stories of people though leveraging down the line to better and better schools though, like hypothetically taking a WUSTL offer to compel a GW offer --> GULC --> Cornell --> Michigan --> Penn --> Chicago but it is a pain in the ass and no guarantee, the best you can do is carpet bomb applications and keep in active communication with the schools once you get in.